There are several KeyDown type events since there may be different controls involve is a cell is actively being edited. (The GridControl may have input focus, or the active cell control like a TextBox might have focus). So, catching keystrokes may depend upon exactly what control has focus.
If you want to catch them no matter what control has the input focus, you might use the CurrentCellKeyDown event. Here is a handler that ignores any arrow key.
Private Sub gridControl1_CurrentCellKeyDown(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyEventArgs) Handles gridControl1.CurrentCellKeyDown
If e.KeyCode = Keys.Up Or e.KeyCode = Keys.Down Or e.KeyCode = Keys.Left Or e.KeyCode = Keys.Right Then
e.Handled = True ''ignore
End If
End Sub